Multilevel converters are used in many high power applications for controlling active and reactive power at medium and high system voltages, such as in HVDC (High-Voltage, Direct Current) and FACTS (Flexible Alternating Current Transmission Systems) applications. A common multilevel converter comprises full-bridge switching cells, or H-bridges, each comprising four semiconductor switches and one capacitor, wherein the switching cells are arranged in chain links, one for each phase, and connected to the power system voltage via an inductor. The chain links are connected in a wye or delta configuration between the phases of the power system. FIG. 1 illustrates a chain link according to prior art comprising a number of switching cells SC1-SCn, each comprising four switches S1-S4 and a capacitor C.
In carrier-based modulation, the switching cells are controlled in order to synthesize an output voltage in accordance with a reference signal, wherein a carrier wave, usually triangular carrier, is used to determine the switching instants for each switching cell. However, the capacitor voltages may deviate from the nominal voltage, and to balance the capacitors, the on-times are controlled for each capacitor so as to increase or decrease their respective voltages. Such balancing may however create harmonic distortions.
In the article “Predictive Current Control for Multilevel Active Rectifiers With Reduced Switching Frequency”, by Zanchetta, P.; Gerry, D. B.; Monopoli, V. G.; Wheeler, P. W.; in Industrial Electronics, IEEE Transactions on, vol. 55, no. 1, pp. 163, 172, January 2008 (Zanchetta et al), a method of using a reduced switching frequency for H-Bridge multilevel converters is described. The method predicts the state of the control period from the present state and limits the switching between the control periods. This method synthesizes the voltage output with a low harmonic distortion and low switching losses. However, using this modulation strategy does not necessarily provide a good balance of the capacitor voltage levels, and will also provide an unequal distribution of losses among the switches.
A number of requirements should be met for a good modulation strategy including, for example:                A) synthesize the output voltage in accordance with the reference voltage;        B) minimize the switching loss, i.e. minimize the number of times the switching cells are switched;        C) balance the voltage levels of the capacitors;        D) balance the loss distributions among the valves (or switching units), since the switches gets hot during use;        E) provide a satisfactory harmonic performance.        
Thus, the quality of the output voltage should fulfil the voltage reference (A) and have a low harmonic distortion (E). Also, the modulation strategy should address problems that may arise in the converter itself; minimize switching losses (B), balance the capacitors (C) and balance the losses (D).
The control strategy of Zanchetta et al suffers from uneven balances of voltage levels of the capacitors (C), and an unbalanced loss distribution (D).
In the article “Multigoal Heuristic Model Predictive Control Technique Applied to a Cascaded H-Bridge StatCom”, by Christopher D. Townsend, in Power Electronics, IEEE Transactions on, Vol. 27, No. 3, March 2012 (Townsend) an MPC (Model Predictive Control) modulation strategy is presented. The modulation strategy of Townsend provides a satisfying balance also between the voltage levels of the capacitors (C). However, the loss distribution is not handled by this MPC strategy.
There exists many other examples that uses MPC. A main idea with MPC is to predict the behavior of the load current for each possible voltage vector generated by the converter. In general, a cost function that represents the desired behavior of the system is used. The future switching of the converter cells is obtained by minimizing the cost function.
However, a problem with using MPC schemes, such as provided by Townsend, is that it requires many calculations in order to evaluate the cost functions. Townsend uses Heuristic models to lessen the computational load. However, the computational load has an exponential relationship to the number of voltage levels. Therefore the computational load is typically infeasible in FACTS applications that uses more than 8-10 serially connected switching cells.
Thus, a modulation strategy that handles all the requirements A)-E), is needed, and a modulation strategy that does not require an unfeasible amount of computational power is especially needed for converter applications where the number of switching levels are large.